Triangle Seminars

Abstract:
The speaker will show how Ulam's increasing subsequence problem
is connected to a variety of classical integrable systems.

Abstract:
Topological orders are non-symmetry breaking phases of matter, which provide a new paradigm in condensed-matter physics. Their characterization is a major open problem, although considerable progress has been made since the proposal of the topological entanglement entropy. In this talk I will review how topological orders have been proposed to serve as robust quantum memories. Then the dynamical stability of topologically ordered quantum states will be examined. Conditions will be derived on the type of dynamical evolution that allows quantum recurrence and preservation of the initial topological order.

Abstract:
We present a set of functional equations defining the anomalous
dimensions of arbitrary local single trace operators in planar N=4 SYM
theory. It takes the form of a Y-system based on the integrability of
the dual superstring sigma-model on the AdS5 x S5 background. This
Y-system passes some very important tests: it reproduces the full
asymptotic Bethe ansatz at large L, including the dressing factor, and
it confirms all recently found wrapping corrections. We shall also
describe the derivation of these equations in some detail.

Abstract:
The hierarchy problem can be represented as a tension between the
need for a large cut-off scale suggested, for instance, by
flavor physics and the need for a low cut-off scale suggested by
naturalness in electroweak symmetry breaking. I will illustrate
how this tension could be largely alleviated if the Standard
Model flowed to an approximate CFT above the weak scale with a
specific relation among the scaling dimensions of the Higgs
sector fields. To investigate the viability of that scenario one
is led to ask the following simple question: in an arbitrary CFT,
given a scalar operator phi, and the operator S=phi phi defined
as the lowest dimension scalar S which appears in the OPE
phi phi, what is the bound (that is d(S) is smaller than f(d(phi)))
on the scaling dimensions of the two operators? I will present a
derivation of the bound based on general considerations of OPE,
conformal block decomposition, and crossing symmetry. The
function f(d(phi)) is computed numerically. When d(phi) goes to
1, one has f(d(phi))=2+O(sqrt(d(phi)-1)), which shows that the
free theory limit is approached continuously. An analogous bound
can be derived in 2D where some non-trivial consistency check can
be made. I will discuss the relevance of the result for the
hierarchy problem and illustrate the directions of future
investigation.